Reduction of the CP content in the diets of piglets requires supplementation with crystalline essential amino acids (AA). Data on the leucine (Leu) and histidine (His) requirements of young pigs fed low-CP diets are limited and have primarily been obtained from nonlinear models. However, these models do not consider the possible decline in appetite and growth that can occur when pigs are fed excessive amounts of AA such as Leu. Therefore, two dose-response studies were conducted to estimate the standardised ileal digestible (SID) Leu : lysine (Lys) and His : Lys required to optimise the growth performance of young pigs. In both studies, the average daily gain (ADG), average daily feed intake (ADFI) and gain-to-feed ratio (G : F) were determined during a 6-week period. To ensure that the diets had sub-limiting Lys levels, a preliminary Lys dose-response study was conducted. In the Leu study, 60 35-day-old piglets of both sexes were randomly assigned to one of five treatments and fed a low-CP diet (15%) with SID Leu : Lys levels of 83%, 94%, 104%, 115% or 125%. The His study used 120 31-day-old piglets of both sexes, which were allotted to one of five treatments and fed a low-CP diet (14%) with SID His : Lys levels of 22%, 26%, 30%, 34% or 38%. Linear broken-line, curvilinear-plateau and quadratic-function models were used for estimations of SID Leu : Lys and SID His : Lys. The minimum SID Leu : Lys level needed to maximise ADG, ADFI and G : F was, on average, 101% based on the linear broken-line and curvilinear-plateau models. Using the quadratic-function model, the minimum SID Leu : Lys level needed to maximise ADG, ADFI and G : F was 108%. Data obtained from the quadratic-function analysis further showed that a ±10% deviation from the identified Leu requirement was accompanied by a small decline in the ADG (−3%). The minimum SID His : Lys level needed to maximise ADG, ADFI and G : F was 27% and 28% using the linear broken-line and curvilinear-plateau models, respectively, and 33% using the quadratic-function model. The preferred model to estimate the His requirement was the curvilinear-plateau model. However, a 10% reduction in the SID His : Lys level was associated with an 11% reduction in the ADG. In conclusion, the SID Leu : Lys level needed to maximise growth was 108% when using the quadratic-function model as the best-fitting model. The minimum SID His : Lys level required to optimise growth was 28% when using the curvilinear-plateau model as the best-fitting model.